OFFSET
1,1
COMMENTS
The triples of sides (a,b,c) with a < b < c are in increasing order of perimeter = 3*b, and if perimeters coincide, then by increasing order of the smallest side. This sequence lists the c's.
Equivalently: largest side of integer-sided triangles such that b = (a+c)/2 with a < c.
c >= 4 and each largest side c appears floor((c-1)/3) = A002264(c-1) times but not consecutively.
For each c = 5*k, k>=1, there exists exactly one right triangle (3*k, 4*k, 5*k) whose sides a < b < c are in arithmetic progression.
For the corresponding primitive triples and miscellaneous properties and references, see A336750.
REFERENCES
V. Lespinard & R. Pernet, Trigonométrie, Classe de Mathématiques élémentaires, programme 1962, problème B-290 p. 121, André Desvigne.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A336750(n, 3).
EXAMPLE
c = 4 only for the smallest triangle (2, 3, 4).
c = 5 only for Pythagorean triple (3, 4, 5).
c = 6 only for triple (4, 5, 6).
c = 7 for the two triples (3, 5, 7) and (5, 6, 7).
MAPLE
for b from 3 to 30 do
for a from b-floor((b-1)/2) to b-1 do
c := 2*b - a;
print(c);
end do;
end do;
MATHEMATICA
Flatten[Array[2*#-Range[#-Floor[(#-1)/2], #-1] &, 20, 3]] (* Paolo Xausa, Feb 28 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Aug 25 2020
STATUS
approved